Question

The probability of obtaining exactly $r$ heads and $(n-r)$ tails, when we toss $n$ unbiased coins is

• A. $\frac{r}{n}$
• B. $\frac{(n-r)}{n}$
• C. $\frac{C_r^n}{2^n}$
• D. $\frac{C_r^n}{3^n}$

Answer 1

Answer: (C)

$\frac{C_r^n}{2^n}$

When we toss $n$ unbiased coins; selection of exactly $r$ heads from $n$ coins $=C_r^n$; (remaining coins will obtain $(n-r)$ tails)
Total number of ways which we could get by arranging $n$ number of coins is $=2^n$
Probability of obtaining exactly $r$ heads and $(n-r)$ tails is $=\frac{C_r^n}{2^n}$